MCQ

MCQ 11 Mark

If $M$ and $N$ are any two events, the probability that atleast one of them occurs is

A
$P(M)+P(N)-2 P(M \cap N)$
✓
$P(M)+P(N)-P(M \cap N)$
C
$P(M)+P(N)+P(M \cap N)$
D
$P(M)+P(N)+2 P(M \cap N)$

Answer

Correct option: B.

$P(M)+P(N)-P(M \cap N)$

(B) $P(M)+P(N)-P(M \cap N)$
Explanation : If $M$ and $N$ are any two events, then the probability that atleast one of them occurs is
$P(M \cup N)=P(M)+P(N)-P(M \cap N)$

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MCQ 21 Mark

The probability that atleast one of the events $A$ and $B$ occurs is 0.6 . If $A$ and $B$ occur simultaneously with probability 0.2 , then $P(\bar{A})+P(\bar{B})$ is equal to :

A
0.4
B
0.8
✓
1.2
D
1.6

Answer

Correct option: C.

1.2

(C) 1.2
Explanation : Given,
$P(A \cup B)=0.6 \text { and } P(A \cap B)=0.2$
We know that,
$P(A \cup B)=P(A)+P(B)-P(A \cap B)$
$\Rightarrow \quad 0.6=P(A)+P(B)-0.2$
$\Rightarrow \quad P(A)+P(B)=0.8$
$\Rightarrow\quad [1-P(\bar{A})]+[1-P(\bar{B})]=0.8$
$\Rightarrow \quad 2-[P(\bar{A})+P(\bar{B})]=0.8$
$\Rightarrow \quad P(\bar{A})+P(\bar{B})=2-0.8=1.2$

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MCQ 31 Mark

If the probabilities for A to fail in an examination is 0.2 and that for $B$ is 0.3 , then the probability that either $A$ or $B$ fails is

A
$>0.5$
B
0.5
✓
$\leq 0.5$
D
$0$

Answer

Correct option: C.

$\leq 0.5$

(C) $\leq 0.5$
Explanation : Given,
$P(A$ fails $)=0.2$
and $ P(B$ fails $)=0.3$
$\begin{aligned} \therefore P(\text { either } A \text { fails or } B \text { fails }) & \leq P(A \text { fails })+P(B \text { fails }) \\ \leq & 0.2+0.3 \\ \leq & 0.5\end{aligned}$

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MCQ 41 Mark

If a single letter is selected at random from the word 'PROBABILITY', then the probability of vowels is

A
$\frac{1}{3}$
✓
$\frac{4}{11}$
C
$\frac{2}{11}$
D
$\frac{3}{11}$

Answer

Correct option: B.

$\frac{4}{11}$

(B) $\frac{4}{11}$
Explanation : Total number of alphabets in the word 'PROBABILITY' $=11$
Number of vowels $=4$
$\therefore$ Required probability $=\frac{4}{11}$

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Applied Maths MCQ

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